Homework Help: Integration by partial fractions

1. Jun 28, 2004

Spectre32

Ok this is the Integral:

(x^2-1)/((x+2)^2(x+3))

Now What i did is break this up into the A + B+C ...etc etc and i came to this:

A/(x+2)^2 + Bx+C/(x+2) + D/X+3.... Now i know i gotta use systems of equations but i've been working on this for like 40 mins and i still can't get it straight. If any one can help me power through this i should then be set.

2. Jun 28, 2004

Parth Dave

multiply everything by (x+2)^2(x+3). After that if you set x=-3 than everything will cancel out except D, which you can than solve for. If you set x=-3 you can create an equation that you can solve for later.

Here comes the annoying part. Expand everything out. Than group everything that has the same degree polynomial (ie group everything that is x^2, x^1, x^0) and factor out the x term. You'll notice that all of this must be equal to x^2-1. Thus, whatever you have infront of x^2 must be 1. Whatever you have infront of x must be 0. Everything else would have to be -1. You have a bunch of equations and 3 more variables to solve for. Enjoy.

i got A=0, D=8, C=-7, B=3.

3. Jun 28, 2004

Hurkyl

Staff Emeritus
(Note to Spectre: you need to be more careful about using parentheses)

Why do you have (Bx + C) / (x + 2)?

4. Jun 29, 2004

Parth Dave

Its supposed to be (Ax + B) / (x + 2)^2 + C/(x + 2) + D/(x + 3)...

5. Jun 29, 2004

Hurkyl

Staff Emeritus
Why do you have (Ax + B) / (x + 2)^2?

6. Jul 6, 2004

Spectre32

Yeah I know.... i broke it up and then everything went to plan.. thanks.